Folded hypercube is a well-known variation of the hypercube structure and can be constructed from a hypercube by adding a link to every pair of nodes with complementary addresses. Let FFv (respectively, FFe) be the set of faulty nodes (respectively, faulty links) in an n-dimensional folded hypercube FQn. Fu has showed that FQn−FFv−FFe for n⩾3 contains a fault-free cycle of length at least 2n−2|FFv| if |FFv|+|FFe|⩽2n−4 and |FFe|⩽n−1. In this paper, we further consider the constraints |FFv|+|FFe|⩽2n−4 and |FFe|⩾n that were not covered by Fu's result. We obtain the same lower bound of the longest fault-free cycle length, 2n−2|FFv|, under the constraints that (1) |FFv|+|FFe|⩽2n−4 and (2) every node in FQn is incident to at least two fault-free links.